Chapter 10 Notes - Chapter 10 Statistical Inference about...

Chapter 10Statistical Inference about Means and Proportions with Two PopulationsOutline:•Estimation of the difference between means of two populations:1.Point estimator of the difference between the means of the populations.2.Sampling distribution of the point estimator.3.Interval estimate of μ1-μ2: Large Sample Case.4.Interval estimate of μ1-μ2: Small Sample Case.•Hypothesis tests about the difference between the means of two populations: Independent Samples.•Inferences about the difference of means: Matched Samples.Point Estimator for μ1-μ21.Select a simple random sample of size n1from population 1 and compute.2.Select a simple random sample of size n2from population 2 and compute.3.Compute the point estimator:.

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Sampling Distribution of :Expected Value of:The point estimator of the difference of means () is Standard Deviation of:(Aside) An easier way to remember is thatwhereσ1= standard deviation of population 1σ2= standard deviation of population 2n1= sample size from population 1n2= sample size from population 2Interval Estimate of μ1-μ2: Large Sample (n1>30 andn2>30)•σ1known and σ2known

where 1-αis the confidence coefficient•σ1unknown and σ2unknownwhere

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Example: Par, Inc.Par, Inc. is a manufacturer of golf equipment and has developed a new golf ball to provide extra distance. In a test of the driving distance using a mechanical device, a sample of golf balls was compared with a sample of golf balls from a competitor (Rap, Ltd.)•Sample StatisticsSample #1Sample #2Par, Inc. Rap, Ltd.Sample Sizen1= 120 ballsn2= 80 ballsMean= 235 yards= 218 yardsStandard Dev.s1= 15 yardss2= 20 yards•Point Estimate of the difference between the populations, where μ1is the mean driving distance of golf balls from Par, Inc.;

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